| 46-XX | | Prev: 45 | Up: Top | Next: 47 | |
| Functional analysis | |
| {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} |
46-00
| General reference works (handbooks, dictionaries, bibliographies, etc.)
| 46-01
| Instructional exposition (textbooks, tutorial papers, etc.)
| 46-02
| Research exposition (monographs, survey articles)
| 46-03
| Historical (must also be assigned at least one classification number from Section 01)
| 46-04
| Explicit machine computation and programs (not the theory of computation or programming)
| 46-06
| Proceedings, conferences, collections, etc.
| |
46Axx
| Topological linear spaces and related structures {For function spaces, see 46Exx}
| 46A03 |
General theory of locally convex spaces
| 46A04 |
Locally convex Fréchet spaces and (DF)-spaces
| 46A08 |
Barrelled spaces, bornological spaces
| 46A11 |
Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
| 46A13 |
Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
[xref: 46M40]
| 46A16 |
Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
| 46A17 |
Bornologies and related structures; Mackey convergence, etc.
| 46A19 |
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R}$, etc.)
| 46A20 |
Duality theory
| 46A22 |
Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
[xref: 39B82, 46M10]
| 46A25 |
Reflexivity and semi-reflexivity [See also 46B10]
[xref: 46B10]
| 46A30 |
Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
| 46A32 |
Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
[xref: 46B28, 46M05, 47L05]
| 46A35 |
Summability and bases [See also 46B15]
[xref: 40J05, 46B15]
| 46A40 |
Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]
[xref: 06F20, 46B40, 46B42]
| 46A45 |
Sequence spaces (including Köthe sequence spaces) [See also 46B45]
[xref: 46B45]
| 46A50 |
Compactness in topological linear spaces; angelic spaces, etc.
| 46A55 |
Convex sets in topological linear spaces; Choquet theory [See also 52A07]
[xref: 47L07, 52A07]
| 46A61 |
Graded Fréchet spaces and tame operators
| 46A63 |
Topological invariants ((DN), ($\Omega$), etc.)
| 46A70 |
Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
| 46A80 |
Modular spaces
| 46A99 |
None of the above, but in this section
| |
46Bxx
| Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see 46Exx}
[xref: 52A21]
| 46B03 |
Isomorphic theory (including renorming) of Banach spaces
| 46B04 |
Isometric theory of Banach spaces
| 46B07 |
Local theory of Banach spaces
| 46B08 |
Ultraproduct techniques in Banach space theory [See also 46M07]
[xref: 46M07]
| 46B09 |
Probabilistic methods in Banach space theory [See also 60Bxx]
| 46B10 |
Duality and reflexivity [See also 46A25]
[xref: 46A25]
| 46B15 |
Summability and bases [See also 46A35]
[xref: 40J05, 46A35]
| 46B20 |
Geometry and structure of normed linear spaces
| 46B22 |
Radon-Nikodym, Krein-Milman and related properties [See also 46G10]
[xref: 46G10]
| 46B25 |
Classical Banach spaces in the general theory
| 46B26 |
Nonseparable Banach spaces
| 46B28 |
Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
[xref: 46A32, 46M05, 47L05]
| 46B40 |
Ordered normed spaces [See also 46A40, 46B42]
[xref: 46A40, 46B42]
| 46B42 |
Banach lattices [See also 46A40, 46B40]
[xref: 46A40, 46B40]
| 46B45 |
Banach sequence spaces [See also 46A45]
[xref: 46A45]
| 46B50 |
Compactness in Banach (or normed) spaces
| 46B70 |
Interpolation between normed linear spaces [See also 46M35]
[xref: 46C07, 46M35]
| 46B99 |
None of the above, but in this section
| |
46Cxx
| Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx}
| 46C05 |
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
| 46C07 |
Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges,...) [See 46B70, 46M35]
| 46C15 |
Characterizations of Hilbert spaces
| 46C20 |
Spaces with indefinite inner product (Krein spaces, Pontryagin spaces,...) [See also 47B50]
| 46C50 |
Generalizations of inner products (semi-inner products, partial inner products, etc.)
[xref: 47B50]
| 46C99 |
None of the above, but in this section
| |
46Exx
| Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10}
[xref: 30H05, 32A37, 32A70, 54C35]
| 46E05 |
Lattices of continuous, differentiable or analytic functions
| 46E10 |
Topological linear spaces of continuous, differentiable or analytic functions
[xref: 46F05]
| 46E15 |
Banach spaces of continuous, differentiable or analytic functions
| 46E20 |
Hilbert spaces of continuous, differentiable or analytic functions
| 46E22 |
Hilbert spaces with reproducing kernels (=[proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
[xref: 47B32]
| 46E25 |
Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}
[xref: 46J10, 46Jxx]
| 46E27 |
Spaces of measures [See also 28A33, 46Gxx]
[xref: 28A33]
| 46E30 |
Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
| 46E35 |
Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
[xref: 46F05]
| 46E39 |
Sobolev (and similar kinds of) spaces of functions of discrete variables
| 46E40 |
Spaces of vector- and operator-valued functions
[xref: 26E20]
| 46E50 |
Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]
[xref: 46G20, 46G25]
| 46E99 |
None of the above, but in this section
| |
46Fxx
| Distributions, generalized functions, distribution spaces [See also 46T30]
[xref: 46T30]
| 46F05 |
Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]
[xref: 46Exx]
| 46F10 |
Operations with distributions
| 46F12 |
Integral transforms in distribution spaces [See also 42-XX, 44-XX]
| 46F15 |
Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]
[xref: 32A45]
| 46F20 |
Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]
| 46F25 |
Distributions on infinite-dimensional spaces [See also 58C35]
| 46F30 |
Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
| 46F99 |
None of the above, but in this section
| |
46Gxx
| Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]
[xref: 35R15, 46E27]
| 46G05 |
Derivatives [See also 46T20, 58C20, 58C25]
[xref: 26E15, 46T20, 49J50, 49J52, 58C20]
| 46G10 |
Vector-valued measures and integration [See also 28Bxx, 46B22]
[xref: 26E20, 28B05, 46B22]
| 46G12 |
Measures and integration on abstract linear spaces [See also 28C20, 46T12]
[xref: 28C20, 28Cxx, 46T12]
| 46G15 |
Functional analytic lifting theory [See also 28A51]
[xref: 28A51]
| 46G20 |
Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]
[xref: 46E50, 46G25, 46T25, 58B12]
| 46G25 |
(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]
[xref: 46E50, 47H60]
| 46G99 |
None of the above, but in this section
| |
46Hxx
| Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20}
| 46H05 |
General theory of topological algebras
| 46H10 |
Ideals and subalgebras
| 46H15 |
Representations of topological algebras
| 46H20 |
Structure, classification of topological algebras
| 46H25 |
Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
| 46H30 |
Functional calculus in topological algebras [See also 47A60]
| 46H35 |
Topological algebras of operators [See mainly 47Lxx]
| 46H40 |
Automatic continuity
| 46H70 |
Nonassociative topological algebras [See also 46K70, 46L70]
[xref: 17C65, 46K70, 46L70]
| 46H99 |
None of the above, but in this section
| |
46Jxx
| Commutative Banach algebras and commutative topological algebras [See also 46E25]
[xref: 32A65]
| 46J05 |
General theory of commutative topological algebras
| 46J10 |
Banach algebras of continuous functions, function algebras [See also 46E25]
[xref: 32A38, 54C40]
| 46J15 |
Banach algebras of differentiable or analytic functions, ${H}^p$-spaces [See also 30D55, 30H05, 32A35, 32A37, 32A38, 42B30]
[xref: 30H05, 32A35, 32A38]
| 46J20 |
Ideals, maximal ideals, boundaries
| 46J25 |
Representations of commutative topological algebras
| 46J30 |
Subalgebras
| 46J40 |
Structure, classification of commutative topological algebras
| 46J45 |
Radical Banach algebras
| 46J99 |
None of the above, but in this section
| |
46Kxx
| Topological (rings and) algebras with an involution [See also 16W10]
[xref: 16W10]
| 46K05 |
General theory of topological algebras with involution
| 46K10 |
Representations of topological algebras with involution
| 46K15 |
Hilbert algebras
| 46K50 |
Nonselfadjoint (sub)algebras in algebras with involution
| 46K70 |
Nonassociative topological algebras with an involution [See also 46H70, 46L70]
[xref: 46H70, 46L70]
| 46K99 |
None of the above, but in this section
| |
46Lxx
| Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.) [See also 22D25, 47Lxx]
[xref: 22D25, 47Lxx, 81R15]
| 46L05 |
General theory of $C^*$-algebras
[xref: 58J22]
| 46L06 |
Tensor products of $C^*$-algebras
| 46L07 |
Operator spaces and completely bounded maps [See also 47L25]
[xref: 47L25]
| 46L08 |
$C^*$-modules
| 46L09 |
Free products of $C^*$-algebras
| 46L10 |
General theory of von Neumann algebras
[xref: 58J22]
| 46L30 |
States
| 46L35 |
Classifications of $C^*$-algebras, factors
| 46L37 |
Subfactors and their classification
| 46L40 |
Automorphisms
| 46L45 |
Decomposition theory for $C^*$-algebras
| Noncommutative measure, integration and probability 46L51 |
Noncommutative measure and integration
| 46L52 |
Noncommutative function spaces
| 46L53 |
Noncommutative probability and statistics
| 46L54 |
Free probability and free operator algebras
| 46L55 |
Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
[xref: 37A55]
| 46L57 |
Derivations, dissipations and positive semigroups in $C^*$-algebras
| 46L60 |
Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]
| 46L65 |
Quantizations, deformations
| 46L70 |
Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]
[xref: 17C65, 46H70, 46K70]
| 46L80 |
$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
[xref: 18F25, 18G60, 46M20, 58J20, 58J22]
| 46L85 |
Noncommutative topology [See also 58B32, 58B34, 58J22]
[xref: 81T75]
| 46L87 |
Noncommutative differential geometry [See also 58B32, 58B34, 58J22]
[xref: 81T75]
| 46L89 |
Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
| 46L99 |
None of the above, but in this section
| |
46Mxx
| Methods of category theory in functional analysis [See also 18-XX]
[xref: 43A95]
| 46M05 |
Tensor products [See also 46A32, 46B28, 47A80]
[xref: 46A32, 46B28, 47A80]
| 46M07 |
Ultraproducts [See also 46B08, 46S20]
[xref: 46B08]
| 46M10 |
Projective and injective objects [See also 46A22]
[xref: 46A22]
| 46M15 |
Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}
[xref: 46M20]
| 46M18 |
Homological methods (exact sequences, right inverses, lifting, etc.)
[xref: 46M20]
| 46M20 |
Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]
[xref: 14F05, 46L80, 55Rxx, 58J22]
| 46M35 |
Abstract interpolation of topological vector spaces [See also 46B70]
[xref: 46B70, 46C07]
| 46M40 |
Inductive and projective limits [See also 46A13]
[xref: 46A13]
| 46M99 |
None of the above, but in this section
| |
46Nxx
| Miscellaneous applications of functional analysis [See also 47Nxx]
[xref: 47Nxx]
| 46N10 |
Applications in optimization, convex analysis, mathematical programming, economics
| 46N20 |
Applications to differential and integral equations
| 46N30 |
Applications in probability theory and statistics
| 46N40 |
Applications in numerical analysis [See also 65Jxx]
| 46N50 |
Applications in quantum physics
[xref: 46L60]
| 46N55 |
Applications in statistical physics
[xref: 46L60]
| 46N60 |
Applications in biology and other sciences
| 46N99 |
None of the above, but in this section
| |
46Sxx
| Other (nonclassical) types of functional analysis [See also 47Sxx]
[xref: 47Sxx]
| 46S10 |
Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]
[xref: 12J25, 12J27]
| 46S20 |
Nonstandard functional analysis [See also 03H05]
[xref: 03H05, 46M07]
| 46S30 |
Constructive functional analysis [See also 03F60]
[xref: 03F60]
| 46S40 |
Fuzzy functional analysis [See also 03E72]
| 46S50 |
Functional analysis in probabilistic metric linear spaces
| 46S60 |
Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50]
| 46S99 |
None of the above, but in this section
| |
46Txx
| Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]
[xref: 46Gxx, 47Jxx, 58Cxx, 58Dxx]
| 46T05 |
Infinite-dimensional manifolds [See also 53Axx, 58Bxx, 58Dxx, 57N20]
| 46T10 |
Manifolds of mappings
[xref: 58D15]
| 46T12 |
Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX]
[xref: 46G12, 58D20]
| 46T20 |
Continuous and differentiable maps [See also 46G05]
[xref: 46G05, 47J07]
| 46T25 |
Holomorphic maps [See also 46G20]
[xref: 46G20]
| 46T30 |
Distributions and generalized functions on nonlinear spaces [See also 46Fxx]
[xref: 46Fxx]
| 46T99 |
None of the above, but in this section
| |